UC Riverside

Given a linear system (L,V) on a smooth algebraic curve X, the classical de Jonquieres' formula gives the number of divisors of degree n of the form D=a_1D_1+...+a_kD_k, where degD_i=n_i and a_1n_1+...+a_kn_k=n, contained in this system, provided this number is finite. In this dissertation we verify the de Jonquieres' formula for a curve and get some de Jonquieres' formulas for a family of nodal curves using Module theorem, Splitting principle, and Transfer theorems.